Algebra.NormedSpace.Euclidean

Abstraction of normed vector spaces

Documentation

class (C a, C a v) => Sqr a v where

Helper class for C that does not need an algebraic type a.

Minimal definition: normSqr

Methods

normSqr :: v -> a

Square of the Euclidean norm of a vector. This is sometimes easier to implement.

Instances

Sqr Double Double

Defined in Algebra.NormedSpace.Euclidean

Methods

normSqr :: Double -> Double

Sqr Float Float

Defined in Algebra.NormedSpace.Euclidean

Methods

normSqr :: Float -> Float

Sqr Int Int

Defined in Algebra.NormedSpace.Euclidean

Methods

normSqr :: Int -> Int

Sqr Integer Integer

Defined in Algebra.NormedSpace.Euclidean

Methods

normSqr :: Integer -> Integer

(Sqr a v, RealFloat v) => Sqr a (Complex v)

Defined in Algebra.NormedSpace.Euclidean

Methods

normSqr :: Complex v -> a

Sqr a v => Sqr a [v]

Defined in Algebra.NormedSpace.Euclidean

Methods

normSqr :: [v] -> a

Sqr a b => Sqr a (T b)

Defined in Number.Complex

Methods

normSqr :: T b -> a

Sqr a b => Sqr a (T b)

Defined in Number.Quaternion

Methods

normSqr :: T b -> a

(Sqr a v0, Sqr a v1) => Sqr a (v0, v1)

Defined in Algebra.NormedSpace.Euclidean

Methods

normSqr :: (v0, v1) -> a

(Ord i, Eq a, Eq v, Sqr a v) => Sqr a (Map i v)

Defined in MathObj.DiscreteMap

Methods

normSqr :: Map i v -> a

(Sqr a v0, Sqr a v1, Sqr a v2) => Sqr a (v0, v1, v2)

Defined in Algebra.NormedSpace.Euclidean

Methods

normSqr :: (v0, v1, v2) -> a

(C a, C a) => Sqr (T a) (T a)

Defined in Algebra.NormedSpace.Euclidean

Methods

normSqr :: T a -> T a

Sqr a v => Sqr (T a) (T v)

Defined in MathObj.Wrapper.NumericPrelude

Methods

normSqr :: T v -> T a

normSqrFoldable :: (Sqr a v, Foldable f) => f v -> a

Default definition for normSqr that is based on Foldable class.

normSqrFoldable1 :: (Sqr a v, Foldable f, Functor f) => f v -> a

Default definition for normSqr that is based on Foldable class and the argument vector has at least one component.

class Sqr a v => C a v where

A vector space equipped with an Euclidean or a Hilbert norm.

Minimal definition: norm

Methods

norm :: v -> a

Euclidean norm of a vector.

Instances

C Double Double

Defined in Algebra.NormedSpace.Euclidean

Methods

norm :: Double -> Double

C Float Float

Defined in Algebra.NormedSpace.Euclidean

Methods

norm :: Float -> Float

C Int Int

Defined in Algebra.NormedSpace.Euclidean

Methods

norm :: Int -> Int

C Integer Integer

Defined in Algebra.NormedSpace.Euclidean

Methods

norm :: Integer -> Integer

(C a, Sqr a v, RealFloat v) => C a (Complex v)

Defined in Algebra.NormedSpace.Euclidean

Methods

norm :: Complex v -> a

(C a, Sqr a v) => C a [v]

Defined in Algebra.NormedSpace.Euclidean

Methods

norm :: [v] -> a

(C a, Sqr a b) => C a (T b)

Defined in Number.Complex

Methods

norm :: T b -> a

(C a, Sqr a b) => C a (T b)

Defined in Number.Quaternion

Methods

norm :: T b -> a

(C a, Sqr a v0, Sqr a v1) => C a (v0, v1)

Defined in Algebra.NormedSpace.Euclidean

Methods

norm :: (v0, v1) -> a

(Ord i, Eq a, Eq v, C a, Sqr a v) => C a (Map i v)

Defined in MathObj.DiscreteMap

Methods

norm :: Map i v -> a

(C a, Sqr a v0, Sqr a v1, Sqr a v2) => C a (v0, v1, v2)

Defined in Algebra.NormedSpace.Euclidean

Methods

norm :: (v0, v1, v2) -> a

C a v => C (T a) (T v)

Defined in MathObj.Wrapper.NumericPrelude

Methods

norm :: T v -> T a

defltNorm :: (C a, Sqr a v) => v -> a

Instances for atomic types

Instances for composed types